Journal
PHYSICAL REVIEW B
Volume 72, Issue 8, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.72.085113
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We discuss Ward identities for strongly interacting fermion systems described by Eliashberg-type theories. We show that Ward identities are not in conflict with the Migdal theorem and derive diagrammatically a Ward identity for a charge vertex both in a Fermi liquid and when a Fermi liquid is destroyed at quantum criticality. We argue that a Ward identity for the spin vertex cannot be obtained within the Eliashberg theory.
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